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nathancarter / group-explorer

Group theory visualization software in the browser
http://nathancarter.github.io/group-explorer/index.html
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Z_3 semidirect product Z_4 error #15

Closed paultpearson closed 3 years ago

paultpearson commented 3 years ago

The presentation for Z_3 semidirect product Z_4 on the webpage

https://nathancarter.github.io/group-explorer/GroupExplorer.html

is not consistent with the multiplication table for that group found at

https://nathancarter.github.io/group-explorer/Multtable.html?groupURL=https://nathancarter.github.io/group-explorer/groups/Z_3%20sdp%20Z_4.group

In particular, the relations a^4 = b^3 = e, bab=a should probably be a^4=3, b^3=a^2, bab=a.

paultpearson commented 3 years ago

Typo correction: a^4 = e.

paultpearson commented 3 years ago

This page also has the same error in the group presentation:

https://nathancarter.github.io/group-explorer/GroupInfo.html?groupURL=https://nathancarter.github.io/group-explorer/groups/Z_3%20sdp%20Z_4.group

rayellis4 commented 3 years ago

You're absolutely right -- good catch! The relation is read from a data file and just displayed, not used in any computations, so it's an easy fix. It's been wrong pretty much since day 1. You might be interested, there is a GE3 routine in development that determines a (roughly) minimal set of relations, and for this group it calculates a⁴ = 1, a²b³= 1, bab = a very much as you suggested. Guess I'm going to have to check the rest of the groups more closely now :-) Thanks again for your help, feel free to bring up any other issues you find. I'm going to close this one.